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Melts and Fluids

Melts and Fluids. Lars Stixrude. Earth’s Interior. Mantle. Oxides & Silicates. Outer Core. Solid. Iron Alloy. Liquid. Solid. Inner Core. Depth 0 660 2890 5150 6371 km

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Melts and Fluids

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  1. Melts and Fluids Lars Stixrude

  2. Earth’s Interior Mantle Oxides & Silicates Outer Core Solid Iron Alloy Liquid Solid Inner Core Depth 0 660 2890 5150 6371 km Pressure 0 24 136 329 363 GPa Temperature 300 1800 3000 5500 6000 K

  3. Melting and differentiation Oxide wt % Mantle Oceanic Crust Continental Crust SiO2 44.9 47.8 58.0 MgO 42.6 17.8 3.5 FeO 7.9 9.0 7.5 Al2O3 1.4 12.1 18.0 CaO 0.8 11.2 7.5 Na2O 0.11 1.31 3.5 K2O 0.04 0.03 1.5 Mean Atomic 21.1 21.6 21.1 Mass Maaløe and Aoki (1977) Elthon (1979) Taylor and McLennan (1985)

  4. Incompatibility • Ionic radius • e.g. alkalis are large • Structure of coexisting crystals • e.g. garnet retains incompatibles much more completely than other phases • Garnet signature of MORB • MORB genesis begins at depths > 80 km

  5. Melting and differentiation Oxide wt % Mantle Oceanic Crust Continental Crust SiO2 44.9 47.8 58.0 MgO 42.6 17.8 3.5 FeO 7.9 9.0 7.5 Al2O3 1.4 12.1 18.0 CaO 0.8 11.2 7.5 Na2O 0.11 1.31 3.5 K2O 0.04 0.03 1.5 Mean Atomic 21.1 21.6 21.1 Mass Maaløe and Aoki (1977) Elthon (1979) Taylor and McLennan (1985)

  6. Magma Dynamics • Driving Force • Liquid-solid density contrast~10 % • Volume • Composition 1600 K Temperature Melting Curve . • Cause of Melting • Decompression 100 km . Geotherm • Result: Differentiation • Liquid enriched in Fe, Ca, Si • Depleted in Mg Depth

  7. Liquid-solid density contrast Driving force for mantle differentiation Why are liquids less dense? Not composition: Mean atomic mass similar

  8. Temperature Origin of melt Melting Curve . 100 km . Geotherm Depth Melting point varies rapidly with depth Controlled by Clapeyron equation dT/dP =V/S~4 K/km Large V! Geotherm controlled by Grüneisen parameter of solids ~1 Geothermal gradient small ~0.5 K/km

  9. Compressibility • Silicate liquids have much larger volume per atom than solids of the same composition • Materials with large volume per atom tend to be more compressible (smaller bulk modulus) • Material Bulk modulus • Basalt liquid 12 GPa • Olivine 129 GPa • Orthopyroxene 106 GPa • Clinopyroxene 114 GPa • Garnet 170 GPa • MgSiO3 perovskite 251 GPa

  10. Liquid-solid density inversion Stolper et al. (1981) JGR

  11. Liquid-crystal density inversion Implications Maximum depth from which magma can be extracted Deeper melt may sink, or remain at depth of origin Olivine flotation in early magma ocean Complications Many components have a large influence on melt density e.g. H2O

  12. Silicate Liquid Structure Si-O polyhedra Mg ions Stixrude & Karki (2005) Science

  13. Silicate liquid structure Local order largely preserved Coordination numbers are similar Si-O ~ 4 Mg-O ~ 5 (less than crystal: volume contrast) Most O shared by two tetrahedra (NBO/T ~ 2) Long-range order destroyed No more infinite chains

  14. Silicate liquid structure Coordination number • Radial distribution function g( r) • Probability of finding two atoms at separation r • Unity for ideal gas • Series of delta functions for solid • Liquid: short range order, long-range disorder

  15. Deep Melt • Melting temperature • Liquid-solid density contrast • Viscosity • Structure • Giant Impact, early evolution of Earth • Komatiites, exotic xenoliths • Ultra-low velocity zone

  16. MgSiO3 Phase Diagram

  17. Structure and thermodynamics • Coordination change • At what pressure? • Over what interval of pressure? • Over what range of coordination number? • Structure within transition interval • Implications • Liquid-solid density contrast • Melting slope • Transport properties Crystal 6 Mean Si-O Coordination number Liquid? 4 Pressure

  18. Liquid Structure Si-O polyhedra Mg ions VVX=1.0 T=3000 K V/VX=0.5 T=3000 K

  19. Silicate Liquid Structure Si-O polyhedra Mg ions

  20. Si-O coordination number • Increases linearly with compression • No detectable T dependence along isochores • No identifiable transition interval (inflection weak or absent) • 5-fold coordinated Si are common at intermediate pressure Stixrude & Karki (2005) Science

  21. Heat Capacity • Silicate liquid • 4.1 to 3.6 • Decreases on compression • T dependence not detected • Dulong-Petit = 3 • Ideal Gas = 2/3

  22. Ab initio melting curve • Integrate Clapeyron equation • V, H from FPMD • Assume one fixed point • 25 GPa, 2900 K Stixrude & Karki (2005) Science

  23. Volume and entropy of melting • Entropy of melting • Nearly constant in lower mantle • Larger than Nk • Volume of melting • Decreases 5-fold • Liquid-solid density contrast • Low P regime: controlled by V • High P regime: controlled by X

  24. Melting in present Earth?

  25. Melts and fluids 14 kbar, 763 C Solubility of water in silicate melt Increases with pressure Complete miscibility achieved at ~ arc conditions 14 kbar, 766 C Shen and Keppler (1997) Nature

  26. In search of the terrestrial hydrosphere • How is water distributed? • Surface, crust, mantle, core • What is the solubility of water in mantle and core? • Can we detect water at depth? • Physics of the hydrogen bond at high pressure? • Has the distribution changed with time? • Is the mantle (de)hydrating? • How is “freeboard” related to oceanic mass? • How does (de)hydration influence mantle dynamics? • Where did the hydrosphere come from? • What does the existence of a hydrosphere tell us about Earth’s origin?

  27. Hydrous Phases Fumagalliite? 10 Å phase Important for carrying water from surface to deep interior Subduction zones Some water removed to melt How much is subducted? How much is retained in the slab? Phase stability Fumagalli et al. (2001) EPSL

  28. Where’s the water? Source of deep water? Surface (subduction) Accretion (chondrites) Chondrites have very large water contents (much greater than Earth) How much of this water could be retained on accretion? Ohtani (2005) Elements

  29. Nominally anhydrous phases • Stishovite • Charge balance: Si4+ -> Al3+ + H+ • Low pressure asymmetric O-H…O • High pressure symmetric O-H-O • Implications for • Elasticity, transport, strength, melting Panero & Stixrude (2004) EPSL

  30. 1.5 1.0 Mass Fraction H2O (%) 0.5 0.0 Nominally anhydrous phases • Primary reservoir of water in mantle? • Incorporation of H requires charge balance • Investigate Al+H for Si in stishovite • End-member (AlOOH) is a stable isomorph • Enthalpy and entropy of solution Solubility Panero & Stixrude (2004) EPSL

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